What are the solutions to the equation (x-3)^4-8(x-3)^2-9=0 ?

The solutions to the equation (x-3)^4-8(x-3)^2-9=0 are x=0,x=6,x=3+i,x=3-i

Find the zeros of (x-3)^4-8(x-3)^2-9=0

The zeros of (x-3)^4-8(x-3)^2-9=0 are x=0,x=6,x=3+i,x=3-i

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(x - 3)^{4} - 8 (x - 3)^{2} - 9 = 0

x = 0, x = 6, x = 3 + i, x = 3 - i

Solution steps

(x - 3)^{4} - 8 (x - 3)^{2} - 9 = 0

Expand

(x - 3)^{4} - 8 (x - 3)^{2} - 9 : x^{4} - 12 x^{3} + 46 x^{2} - 60 x

x^{4} - 12 x^{3} + 46 x^{2} - 60 x = 0

Factor

x^{4} - 12 x^{3} + 46 x^{2} - 60 x : x (x - 6) (x^{2} - 6 x + 10)

x (x - 6) (x^{2} - 6 x + 10) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 6 = 0 or x^{2} - 6 x + 10 = 0

Solve

x - 6 = 0 : x = 6

Solve

x^{2} - 6 x + 10 = 0 : x = 3 + i, x = 3 - i

The solutions are

x = 0, x = 6, x = 3 + i, x = 3 - i

y, y^{2} = x^{3}

y, x^{3} + y^{3} = 1

x^{9} + x^{6} = 36

y, x^{4} + y^{4} = 16

a x^{4} + b x^{2} + c = 0

What are the solutions to the equation (x-3)^4-8(x-3)^2-9=0 ?
The solutions to the equation (x-3)^4-8(x-3)^2-9=0 are x=0,x=6,x=3+i,x=3-i
Find the zeros of (x-3)^4-8(x-3)^2-9=0
The zeros of (x-3)^4-8(x-3)^2-9=0 are x=0,x=6,x=3+i,x=3-i